The Sun claims Neil Warnock is keen on Marriott, who has scored 23 goals in all competitions this season, after the Bluebirds' bids for other strikers faltered.
Marriott has been linked with Leeds United and Hull City during the current transfer window, although Tigers boss Nigel Adkins has denied making any bid for the player.
The Beverley-born striker was denied another goal by a disputed offside call in Peterborough's 0-0 draw at Wigan Athletic on Saturday.
Posh boss McCann was philosophical about the League One club’s chances of holding on to Marriott when he spoke last week.
"It’s important we keep him. But this is Peterborough United, not Manchester United, and we have to cut our cloth accordingly," he said.
"I don’t think the chairman or Barry Fry are trying to sell him, but there is no doubt Jack is way above League One. With his pace and goals, I am sure he could easily play in the Championship, or maybe higher."